Rearranging Differential Equation
Hi, I was going over my notes and didnt understand one of the steps made in a calculation, was hoping someone could explain it to me.
Im trying to find an analytic solution for an ODE: dY/dX + X*Y = X
The integrating factor is I = e^((X^2)/2)
Multiplying the equation with the integrating factor
I*(dY/dX) + X*I*Y = X*I
This next step I dont follow where it gets simplified to:
(d/dX)*(Y*e^((X^2)/2)) = X*(e^((X^2)/2))
The following line's after are:
YI = I
Y = 1 + C*I
Any help would be appriciated, thank you.